Question:
In a theoretical closed system, a Carnot engine operates between two
reservoirs at temperatures $T_1$ and $T_2$ ($T_1 > T_2$). The engine absorbs $Q_1$
amount of heat from the hot reservoir at temperature $T_1$ and rejects $Q_2$
amount of heat to the cold reservoir at temperature $T_2$.
1. Derive the expression for the efficiency ($\eta$) of the Carnot engine.
2. If the temperatures of the hot and cold reservoirs are 600 K and 300 K,
respectively, and the engine absorbs 1000 J of heat from the hot reservoir,
calculate the work done by the engine and the amount of heat rejected to
the cold reservoir.